total set of functionals

A set $\Gamma$ of continuous linear functionals $f(x)$, defined on a linear topological space $X$, such that there is no element $x\in X$, $x\neq0$, on which the equality $f(x)=0$ is satisfied for all $f\in\Gamma$. Every locally convex space has a complete set of functionals.

How to Cite This Entry:
Complete set of functionals. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Complete_set_of_functionals&oldid=32771
This article was adapted from an original article by M.I. Kadets (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article